21N.1.SL.TZ0.1

pestleMathematicsAASLPaper 121N· sl-2-6-quadratic-functionsource ↗

Consider the function $f (x) = - 2 (x - 1) (x + 3)$ , for $x \in ℝ$ . The following diagram shows part of the graph of $f$ .

For the graph of $f$

find the $x$ -coordinates of the $x$ -intercepts.

[2]

a.i.

find the coordinates of the vertex.

[3]

a.ii.

The function $f$ can be written in the form $f (x) = - 2 {(x - h)}^{2} + k$ .

Write down the value of $h$ and the value of $k$ .

[2]

Markscheme / solution

setting $f (x) = 0$ (M1)

$x = 1, x = - 3$ (accept $(1, 0), (- 3, 0)$ ) A1

[2 marks]

a.i.

METHOD 1

$x = - 1$ A1

substituting their $x$ -coordinate into $f$ (M1)

$y = 8$ A1

$(- 1, 8)$

METHOD 2

attempt to complete the square (M1)

$- 2 ({(x + 1)}^{2} - 4)$ (M1)

$x = - 1, y = 8$ A1A1

$(- 1, 8)$

[3 marks]

a.ii.

$h = - 1$ A1

$k = 8$ A1

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]